Iteration Examples in CS Thinking

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Iteration.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in CS Thinking.

Concept Recap

Repeating a block of instructions multiple times until a stopping condition is satisfied. Iteration is one of the three fundamental control structures (along with sequence and selection) and is implemented through while loops, for loops, and other looping constructs.

Do this again and again until some condition is met, then move on to the next step.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Loops let you do repetitive tasks without writing repetitive code.

Common stuck point: The loop must have a way to stop—every iteration should progress toward the stopping condition.

Sense of Study hint: When writing a loop, first decide what action needs repeating and what condition should stop the repetition. Initialize any loop variables before the loop starts, and make sure the loop body changes something so the stopping condition is eventually reached.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Recursion Mistakes

Worked Examples

Example 1

easy

Trace: FOR i = 1 TO 4: OUTPUT i * 2.

Trace: FOR i = 1 TO 4: OUTPUT i * 2

Answer

2, 4, 6, 8

First step

Step 1: i = 1: output 2. i = 2: output 4.

Full solution

2
Step 2: i = 3: output 6. i = 4: output 8.
3
Step 3: Loop ends after i = 4. Outputs: 2, 4, 6, 8.

Iteration (looping) repeats a block of code a specified number of times. A FOR loop is used when we know in advance how many repetitions are needed.

Example 2

medium

Trace: SET count = 0. SET n = 1. WHILE n <= 10: IF n MOD 2 == 0 THEN count = count + 1. n = n + 1. OUTPUT count.

Example 3

medium

Trace nested: for

i

in 1..3: for

j

in 1..2: count += 1. Final count?

Example 4

medium

Trace: count = 0; for

i

in 1..50: if

i \bmod 7 == 0

: count += 1. Final count?

Example 5

medium

Trace:

i = 1

;

s = 0

; while

i \le 5

s = s + i \cdot i

;

i = i + 1

. Final

s

Example 6

medium

Trace: max = -infinity; for

x

[3, 7, 2, 9, 4]

: if

x >

max: max =

x

. Final max?

max = −∞; for x in [3,7,2,9,4]: if x > max: max = x. Final max?

Example 7

medium

Trace:

s = 0

; for

i

in 1..10: if

i \bmod 2 == 1

s = s + i

. Final

s

Example 8

hard

Trace Fibonacci:

a=0, b=1

; repeat 5 times:

t = a + b

;

a = b

;

b = t

. Final

b

Example 9

hard

Trace: list =

[5, 3, 8, 1, 9, 2]

; find min via single pass. What is min?

list = [5,3,8,1,9,2]; find min via single pass. What is min?

Example 10

hard

Trace: list =

[4, 2, 7, 1, 8]

. Compute average via iteration: sum then divide by count.

Example 11

hard

Trace string concatenation:

s =

'' ; for

c

in 'abc':

s = s + c

. Final

s

Example 12

challenge

Trace:

n = 27

; count = 0; while

n > 1

: if

n

even:

n = n // 2

; else:

n = 3 \cdot n + 1

; count += 1. What is count when the loop ends? (Collatz)

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Write pseudocode using a loop to output the numbers 5, 10, 15, 20, 25.

Example 2

easy

Trace this loop: SET total = 2. REPEAT 4 TIMES: SET total = total + 3. OUTPUT total.

Trace: SET total = 2. REPEAT 4 TIMES: total = total + 3. OUTPUT total.

Example 3

easy

Trace:

s=0

; for

i

1,2,3

s=s+i

. Final

s

Example 4

easy

How many times does 'for i in range(5)' run the loop body? (range(5) is 0..4)

Example 5

easy

Trace:

i=0

; while

i < 3

i = i + 1

. Final

i

Trace the while loop; what is final i?

Example 6

easy

Trace: count

=0

; for

x

[4,7,1,9]

: count = count + 1. Final count?

Trace: count = 0; for x in [4, 7, 1, 9]: count = count + 1. Final count?

Example 7

easy

Which keyword typically starts a loop that repeats while a condition is true?

Example 8

easy

Trace:

p=1

; for

i

1,2,3

p = p * 2

. Final

p

Example 9

easy

A loop never updates its condition variable. What problem occurs?

What problem occurs when the condition variable is never updated?

Example 10

easy

Trace: for

i

in range(3): print

i

(range(3) is 0,1,2). What is printed in order?

for i in range(3): print i — what is printed in order?

Example 11

medium

Trace:

s=0

; for

i

in range(1,5):

s=s+i

(range(1,5) is 1,2,3,4). Final

s

Example 12

medium

Nested loops: for

i

in range(3): for

j

in range(2): count+=1. Final count?

Example 13

medium

Trace:

i=10

; while

i > 0

i = i - 3

; print final

i

(when loop ends).

Example 14

medium

How many times does 'for i in range(2, 10, 2)' run? (start 2, stop 10, step 2)

Example 15

medium

A loop sums even numbers in

[1,2,3,4,5,6]

. Trace and give the total.

Example 16

medium

Trace: a list

[1,2,3]

; for each element, append element*element to a new list. What is the new list?

for each element in [1,2,3], append element×element. What is the new list?

Example 17

medium

A while-loop reads numbers until it reads 0 (a sentinel). For inputs 5, 3, 0, how many numbers are processed before stopping?

For inputs 5, 3, 0 — how many numbers are processed before stopping?

Example 18

medium

Trace:

s=0

; for

i

in range(4):

s = s + i

(range(4) is 0,1,2,3). Final

s

Example 19

medium

Trace:

i=1

;

f=1

; while

i \le 3

f = f * i

;

i = i + 1

. Final

f

Example 20

challenge

Trace:

a=0,b=1

; repeat 4 times:

t=a+b

;

a=b

;

b=t

. Final

b

Example 21

challenge

A list

[1,2,3,4]

; a loop removes every element while iterating index 0..len. Why does this skip elements?

Example 22

challenge

Two loops sum 1..n: loop A runs n times, loop B is nested running n*n times. For large n, which dominates the running time and what is B's growth class?

Example 23

easy

Trace:

s=0

; for

i

1,2,3,4

s = s + i

. Final

s

Example 24

easy

How many times does 'for i in range(6)' run the body?

Example 25

easy

Trace:

c=0

; for

x

[2,4,6,8,10]

c = c + 1

. Final

c

Trace: c = 0; for x in [2, 4, 6, 8, 10]: c = c + 1. Final c?

Example 26

easy

Trace:

i = 5

; while

i > 0

i = i - 1

. Final

i

Trace: i = 5; while i > 0: i = i − 1. Final i?

Example 27

easy

Trace:

p = 1

; for

i

1,2,3,4

p = p * i

. Final

p

Example 28

medium

Trace:

s = 0

; for

i

in range(1, 11):

s = s + i

. Final

s

Example 29

medium

How many times does 'for i in range(3, 11, 2)' run?

Example 30

medium

A loop with a 'break' statement that fires after 5 iterations of a planned 100 — how many times does the body execute?

Example 31

medium

What is the difference between break and continue?

Example 32

hard

Why does modifying a list while iterating over it often cause bugs?

Example 33

hard

A nested loop runs an outer loop

n

times and an inner loop

n

times. What is the running time class?

Example 34

hard

A while loop with condition

i < 10

but

i

never changes inside. What problem and what fix?

Example 35

challenge

A program needs to compute

n!

for

n=10

iteratively. Why is iteration preferred over recursion here in many languages?

← Back to Iteration Common Mistakes Practice Mode

Related Concepts

Sequence While Loop For Loop Recursion

Background Knowledge

These ideas may be useful before you work through the harder examples.

sequence